E
eccentricity, numerical
--- curve second order, 207
ellipse, 198
--- hyperbola, 200
--- parabola, 203
edge
--- angle, 150
--- figure, 150
--- graph, 348
--- length, 350
--- valuation, 350
--- multiple, 348
--- sequence, 351
--- cycle, 351
--- directed circuit, 351
--- isolated edge, 351
--- open, 351
--- path, 351
effective rate, 22
eigenfunction, 541
--- differential equation, 515
--- integral equation, 565 , 570
--- normalized, 516
eigenvalue, 278 , 541
--- differential equation, 515
--- integral equation, 565 , 570
--- operator, 622
eigenvalue problem
--- general, 278
--- matrices, 278
--- special, 278
eigenvector, 264 , 278 , 622
Einstein's summation convention, 262
element, 290
--- finite, 914
--- generic, 814
--- linearly independent, 598
--- neutral, 298
--- positive, 601
element of area, plane, table, 474
element of surface, curved, table, 482
element of volume, table, 479
elementary cell
--- crystal lattice, 310
--- non-primitive, 310
--- primitive, 310
elementary formula, predicate logic, 289
elementary surface, parametric form, 482
elementary volume
--- arbitrary coordinates, 479
--- Cartesian coordinates, 476
--- cylindrical coordinates, 477
--- spherical coordinates, 478
elimination method, Gauss, 276
elimination step, 891
ellipse, 198
--- arc, 200
--- area, 199
--- diameter, 198
equation, 198
--- focal properties, 198
--- focus, 198
--- perimeter, 200
--- radius of curvature, 199
--- semifocal chord, 198
--- tangent, 199
--- transformation, 205
--- vertex, 198
ellipsoid, 220
--- central surface, 224
--- cigar form, 220
--- imaginary, 224
--- lens form, 220
--- of revolution, 220
--- surface second order, 224
embedding, canonical, 626
encoding method, RSA, 331
encyphering, 334
endomorphism, linear operators, 601
endpoint, 348
energy
--- particle, 539
--- spectrum, 540
--- system, 538
--- zero-point translational energy, 541
--- zero-point vibration energy, 546
entropy
--- generalized, 825
--- metric, 819
--- topological, 819 , 829
envelope, 236 , 237
epicycloid, 101
--- curtate, 102
--- prolate, 102
epitrochoid, 102
equality
--- asymptotic, 419
--- complex numbers, 34
--- matrices, 254
equality relation
--- identity, 10
equation, 10
--- algebraic, 38 , 43
--- biquadratic, 42
--- characteristic, 278 , 494 , 503 , 505
--- cubic, 40 , 63
--- curve
--- plane, 194 , 225
--- second degree, 205
--- second order, 205
--- defining, 508
--- degree, 38
--- Diophantine, 325
--- linear, 325
ellipse, 198
exponential, solution, 45
--- first degree, 39
--- fourth degree, 42
--- homogeneous, 629
--- hyperbola, 200
--- hyperbolic functions, solution, 46
--- inhomogeneous, 629
--- irrational, 39
--- Korteweg de Vries, 548
--- line
--- plane, 194
--- space, 217
--- linear, 39
--- logarithmic, solution, 46
--- logistic, 798 , 837
--- non-linear
--- fixed point, 884
--- numerical solution, 884
--- normal form, 38
--- n-th degree, 43
--- operator equation, 629
--- parabola, 203
--- Parseval, 422 , 516 , 579 , 618
--- pendulum, 841
--- plane, 214
--- general, 214
--- Hessian normal form, 214
--- intercept form, 215
--- plane curve, 194
--- polynomial
--- numerical solution, 887
--- quadratic, 39 , 62
--- root, definition, 38
--- Schrodinger
--- linear, 538
--- non-linear, 547
--- second degree, 39
--- sine-Gordon, 549
--- solution, general, 38
--- space curve, 214 , 238
--- vector form, 238
--- sphere, 243
--- surface
--- normal form, 220
--- second order, 223
--- space, 213 , 243
--- system of, 38
--- term algebra, 341
--- third degree, 40
--- transcendent, 38
--- trigonometric, solution, 46
--- vector, 187
equation system
--- linear^ 271 , 890
--- overdetermined, 893
--- non-linear, 890 , 896
--- numerical method, iteration, 890
--- numerical solution, 890
--- direct method, 890
--- overdetermined, 277 , 890
--- row echelon form, 890
--- underdetermined, 890
equations
--- Delambre, 166
--- L'Huilier. 167
--- Mollweide, 142
--- Neper, 167
equilibrium point, 797
--- hyperbolic, 804
equivalence, 286
--- class, 297
--- logic, 287
--- proof, 5
--- relation, 296
Eratosthenes sieve, 320
error
--- absolute, 792 , 939
--- absolute maximum error, 792
--- apparent, 790
--- average, 789 , 791
--- computer calculation, 941
--- defined, 792
--- density function, 788
--- discretization, 942
equation, 893
estimation, iteration method, 897
--- input error, 941
--- least mean squares, 421
--- mean, 789
--- square, 790 , 791
--- normally distributed, 788
--- percentage, 792
--- probable, 789 , 791
--- relations between error types, 789
--- relative, 792 , 939
--- relative maximum error, 792
--- round-off, 942
--- single measurement, 790
--- standard, 790
--- true, 790
--- truncation error, 942
--- type 1 error rate, 753
error (continued)
--- type, measurement errors. 788
error analysis, 796
error calculus
--- direct problem, 941
--- inverse problem, 941
error curve, 72
error estimation, mean value theorem, 389
error function, 461
--- Gauss, 759
error integral, Gauss, 461
error orthogonality, 909
error propagation. 794
--- law, 795
error types, computer calculation, 941
ess. sup (essential supremum), 639
Euclidean
--- algorithm, 3 , 14
--- polynomial rings, 315
--- norm, 318
--- vector norm, 258
--- vector space, 318
Euler
--- angle, 211
--- broken line method, 904
--- circuit, 352
--- constant, 460
--- differential equation
--- n-th order, 504
--- variational calculus. 554
--- formula, 247 , 420
--- formulas, 421 , 424
--- function, 331
--- graph, 352
--- integral of the second kind, 459
--- integral, first kind, 1056
--- integral, second kind, 1056
--- numbers, 412
--- polygonal method, 904
--- relation (complex numbers), 35 , 698
--- theorem, 154
--- trail, 352
--- open, 352
Euler-Hierholzer theorem, 352
event, 747
--- certain, 747
--- complete system of, 748 , 750
elementary, 747
--- impossible, 747
--- independent, 750
--- random, 747
--- set of events, 747
--- simple, 747
evolute, 236
evolution
equation, 547
--- function, 547
evolution strategies, 870
evolvent, 236 , 237
--- of circle, 104
excess, spherical triangle, 163
exchange theorem, 395
exchange, cyclic, sides and angles, 141
excluded middle, 287
existential quantifier, 289
expansion
--- Fourier, forms, 423
--- Laplace, 259
--- Laurent, 692
--- Maclaurin, 418
--- Taylor, 389 , 417 , 691
expectation, 753
expected value, 753
--- bivariate distribution, 779
--- two-dimensional distribution, 779
exponent, 7
exponential distribution, 760
exponential function, 71
--- complex, 679
--- general, 699
--- natural, 698
exponential integral, 461
exponential sum, 72
expression
--- algebraic, 10
--- manipulation, 979
--- analytic, 48
--- domain, 48
explicit form, 48
--- implicit form, 48
--- parametric form, 49
--- Boolean, 344
--- concurrent, 345
explicit form, 48
--- finite, 908
--- partial differential equations, 911
--- implicit form, 48
--- integral rational, 11
--- irrational, 11 , 17
--- non-polynomial, manipulation, 981
--- parametric form, 49
--- propositional logic, 286
--- rational, 11 , 14
--- semantically equivalent, 345
--- tautology, 288
--- transcendent, 11
--- vector analysis, 659
extension principle, 368
extension theorem of Hahn, 625
extension, linear functional, 624
extraction of the root
--- complex numbers, 38
--- real numbers, 8
extrapolation principle, 902
extremal, radius of curvature, 558
extreme value, 390
--- absolute, 390
--- determination, 391
--- higher derivatives, 391
--- side conditions, 403
--- sign change, 390
--- function, 401
--- relative, 390
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